Two Tailed Test

The significance level, α, is concentrated in two parts (or tails) symmetrical about the mean.

The limit of acceptance in this case is the corresponding confidence interval for μ or p, that is to say:

or:

Example

It is known that the standard deviation of the scores in a math exam was 2.4 and a sample of 36 students scored an average of 5.6. With this data, can the hypothesis be confirmed that the average test score was 6 with a confidence level of 95%?

One Tailed Test

Case 1

Critical Values

1 - α

α

zα

0.90

0.10

1.28

0.95

0.05

1.645

0.99

0.01

2.33

The significance level, α, is concentrated in one part or tail.

The limit of acceptance in this case is:

or:

Example

A sociologist has predicted that in a given city, the level of absenteeism in the upcoming elections will be a minimum of 40%. From a random sample of 200 individuals from the voting population, 75 state they will likely vote. Determine with a significance level of 1%, if the hypothesis can be accepted.

Example

A report indicates that the maximum price of a plane ticket between New York and Chicago is $120 with a standard deviation of $40. A sample of 100 passengers shows that the average price of their tickets was $128.

Can the above statement be accepted with a significance level equal to 0.1?